According to (), a quantum system with semi-bounded Hamiltonian without instantaneous spreading and without confinement does not have states, which are localized in bounded regions.
This result will now be refined exploiting translational symmetry. It applies to massive and massless relativistic
systems and also to systems with a more general energy-momentum spectrum. Partially we follow Thaller 1992 [1]} minimizing the assumptions.and avoiding an error in [1]} regarding the spectrum of \(H=\lambda (P)\) , as there the assumptions on \(\lambda \)  do not imply that \(\lambda ^{-1}([a,b])\)  is compact Lemma () is a version of Hegerfeldt, Ruijsenaars 1980 [3]}. Let \(S\)  be a representation of the group \(\mathbb {R}^3\)  of spatial translations. To (\(L\,1,2\) ) we add the assumption
